In a dharma talk, Dogen said,

Even if you are speaking rationally and another person says something unreasonable, it is wrong to defeat him by arguing logically. On the other hand, it is not good to give up hastily saying that you are wrong, even though you think that your opinion is reasonable.

Neither defeat him, nor withdraw saying you are wrong. It is best to just leave the matter alone and stop arguing. If you act as if you have not heard and forget about the matter, he will forget too and will not get angry. This is a very important thing to bear in mind.

This is one of the most practical passages (Chapter 1-10) in Shobogenzo Zuimonki. For once, Dogen is not talking about zazen, impermanence, or non-gaining (not that there's anything wrong with that). He's talking about direct action, how we live our life, employing right speech and right action, exercising the kshanti paramita. How we live our life is more important in Zen than what we say, and we express our true understanding of Zen not in our words but in our actions. That's why Dogen emphasizes his point by saying this is a very important thing to bear in mind.

Besides. do we ever really win arguments? Most arguments I've been in (and there have been many), each participant retreats to their own position, defends their original statements, and doesn't really listen to the other, except for waiting for a logical slip or an opportunity to speak again. Usually, both participants walk away from an argument more convinced of their rightness than before the argument started. Better to just move on as Dogen advises.

Dogen was probably talking about arguments over the dharma. All the more reason not to try and employ clever logic to make your point, but also, if you're explaining the real dharma, all the more reason not to give in and say you're wrong. Best to make your point by demonstrating your superior understanding with action and walking away, not clinging to your position or engaging in divisive language.